Tuesday, May 5, 2015

The six year re-alignment period between the lunar line-of-apse and line-of-nodes is set by the planets.


DT = the lunar Draconic year ________=  0.9490 sidereal yrs = 346.620076 days
DP = lunar nodal precession _________= 18.599 sidereal yrs 
AT = the lunar Full Moon Cycle______= 1.1274 sidereal yrs = 411.784430 days
AP= lunar apsidal precession________ = 8.851 sidereal yrs  
AD = alignment period of the lunar line-of-apse and the lunar line-of-nodes = 5.9971 sidereal yrs

where     1 -- 1/AT = 1/AP ,       1/DT -- 1 = 1/DPand  1/AD = 1/DP + 1/AP*** 

and

T= Sidereal orbital period of Jupiter __= 11.8622 sidereal yrs = 4332.75 days
SJS = Synodic period of Jupiter/Saturn  _= 19.859 sidereal yrs               
SVE = Synodic period of Venus/Earth__= 1.5987 sidereal yrs

It can be shown that the apsidal precession period of the lunar orbit is linked to the synodic periods of Venus/Earth and Jupiter/Saturn by the following relationship:


AP ≈ [SJS×10SVE] / [SJS + 10SVE] = 8.857 yrs

[with an error of 0.006 sidereal yrs = 2.2 days] 

and that the lunar nodal precession period is linked to the sidereal orbital period of Jupiter by:


5/4×DT = (1/10)×TJ**

See the following link:

Now this last equation can be rearranged using the relationships (*)  and (**to give: 


DP = TJ / [25/2  -- TJ] = 18.599 yrs


Hence, using the relationship (***), we can see that the six year re-alignment period between the lunar line-of-apse and the lunar line-of-nodes is synchronized with the synodic periods of Venus/Earth and Jupiter/Saturn and the orbital period of Jupiter.


Saturday, April 18, 2015

Will the PDO Turn Positive in the Next Few Years?

Glossary: PDO - Pacific Decadal Oscillation; LOD - Earth's Length of Day

Back in 2008, I wrote a paper entitled:

Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation Rate Externally Driven and Do They Affect Climate? The General Science Journal, Dec 2011, 3811. which can be freely down loaded at:

http://gsjournal.net/Science-Journals/Essays/View/3811

One of the results of this paper concerned the long-term changes in the Pacific Decadal Oscillation (PDO). It predicted that the PDO should return to its positive phase sometime around 2015 - 2017.

A.  The difference between the actual LOD and the nominal LOD value of 86400 seconds.

Page 11 - Figure 4


Figure 4: This figure shows the variation of the Earth's length-of-day (LOD) from 1656 to 2005 (Sidorenkov 2005)[blue curve]. The values shown in the graph are the difference between the actual LOD and the nominal LOD value of 86400 seconds, measured in units of  10^(-5) seconds. Superimposed on this graph are 1st and 3rd order polynomial fits to the change in the Earth's LOD.

B. The absolute deviation of the Earth's LOD from a 1st and 3rd order polynomial fit to the long-term changes in the LOD between 1656 and 2005

page 14 - Figure 7a


Figure 7a: Shows the absolute deviation of the Earth's LOD from a 1st and 3rd order polynomial fit to the long-term changes in the LOD (measured in units of 10^(-5) seconds). There are nine significant peaks in the absolute deviation which are centered on the years 1729, 1757, 1792, 1827, 1869, 1906, 1932, 1956 and 1972. 

C. A comparison between the peak (absolute) deviations of the LOD from its long-term trend and the years where the phase of the PDO [proxy] reconstruction is most positive.

Page 15 - Figure 8


Figure 8: The upper graph shows the PDO reconstruction of D’Arrigo et al. (2001) between 1707 and
1972. The reconstruction has been smoothed with a 15-year running mean filter to eliminate short-term fluctuations. Superimposed on this PDO reconstruction is the instrumental mean annual PDO index (Mantua 2007) which extends the PDO series up to the year 2000. The lower graph shows the absolute deviation of the Earth’s LOD from 1656 to 2005. The data in this figure has also been smoothed with a 15-year running mean filter.

A comparison between the upper and lower graph in figure 8 (above) shows that there is a
remarkable agreement between the years of the peak (absolute) deviations of the LOD from its
long-term trend and the years where the phase of the PDO [proxy] reconstruction is most positive. While the correlation is not perfect, it is convincing enough to conclude the PDO index is another good example of a climate system that is directly associated with changes in the Earth's rotation rate.

If you look closely at the peaks in the deviation of Earth's LOD from its long term trend and the peaks in the PDO index shown in figure 8, you will notice that the peaks in deviation of LOD take place 8 - 10 years earlier (on average) than the peaks in the PDO index, suggesting a causal link.


D. The path of the CM of the Solar System about the Sun in a reference frame that is rotating with the planet Jupiter


Page 17 - Figure 9


 Figure 9: Shows the Sun in a reference frame that is rotating with the planet Jupiter. The perspective is the one you would see if you were near the Sun’s pole. A unit circle is drawn on the left side of this figure to represent the Sun, using an x and y scales marked in solar radii. The position of the CM of the Solar System is also shown for the years 1780 to 1820 A.D. The path starts in the year 1780, with
each successive year being marked off on the curve, as you move in a clockwise direction. This
shows that the maximum asymmetry in the Sun’s motion occurred roughly around 1790-91.

The path of the CM of the Solar System about the Sun that is shown in figure 9 [above] mirrors the typical motion of the Sun about the CM of the Solar System. This motion is caused by the combined gravitational influences of Saturn, Neptune, and to a lesser extent Uranus, tugging on the Sun.

The motion of the CM shown in figure 9 repeats itself roughly once every 40 years. The timing and level of asymmetry of Sun’s motion is set, respectively, by when and how close the path approaches the point (0.95, 0.0), just to the left of the Sub-Jupiter point. Hence, we can quantify the magnitude and timing of the Sun’s asymmetric motion by measuring the distance of the CM from the point (0.95, 0.0).

E. The years where the Suns' motion about the CM of the Solar System is most asymmetric.

Page 18 - Figure 10


Figure 10: shows The distance of the centre-of-mass (CM) of the Solar System (in solar radii) from the point (0.95, 0.00) between 1650 and 2000 A.D. The distance scale is inverted so that top of the peaks correspond to the times when the Sun’s motion about the CM is most asymmetric.

An inspection of figure 10 shows that there are times between 1700 and 2000 A.D. where the CM of the Solar System approaches the point (0.095, 0.00) i.e. at the peaks of the blue curve in figure 10 where the Sun's motion about the CM is most asymmetric. These are centred on the years, 1724, 1753, 1791, 1827, 1869, 1901, 1932, and 1970. Remarkably, these are very close to the years in which the Earth’s LOD experienced its maximum deviation from its long-term trend i.e. the years 1729, 1757, 1792, 1827, 1869, 1906, 1932, 1956 and 1972.   

This raised the possibility that the times of maximum deviation of the Earth's LOD might be related to the times of maximum asymmetry in the Sun’s motion about the CM. 

In addition, if both of these indices precede transitions of the PDO into its positive phase by 8 - 10 years, then it could be possible to use the times of maximum asymmetry in the Sun’s motion about the CM to predict when the PDO will make its next transition into its positive phase.

F. When will the transition to the next positive phase of the PDO take place?




This figure shows the proxy PDO reconstruction of D’Arrigo et al. (2001) between 1707 and 1972 [blue curve]. The reconstruction has been smoothed with a 15-year running mean filter to eliminate short-term fluctuations. Superimposed on this PDO reconstruction is the instrumental mean annual PDO index (Mantua 2007) which extends the PDO series up to the year 2000 [green curve]. Also shown is the proximity of the CM of the Solar System to sub-Jupiter point which measures the asymmetry of the Sun's motion about the CM [orange curve].

Hence, like the long term deviation of the Earth's LOD from its long term trend, the peaks in asymmetry of the Sun's motion about the CM of the Solar System take place roughly 8 - 10 years prior to positive peaks in the PDO index. 

Careful inspection of the figure above shows that Sun's motion about the CM peaks in about 2007 which would indicate that the next transition to a positive PDO phase should take place some time around the years 2015 to 2017.

[Note: The above graph shows a prediction made on the assumption that forward shift between the two curves is of the order of the average length of the Hale sunspot cycle = 11 years. It probably a good indicator of the level of uncertainty of the prediction being made]. 


[Note: I propose that GEAR EFFECT is the underlying reason for the connection between peaks in the asymmetry of the Sun's motion about the Barycentre of the Solar System (SSBM) and the absolute deviation of the Earth rotation rate about it's long-term in crease of ~ 1.7 ms/century. A post describing the GEAR EFFECT can be found here:]

http://astroclimateconnection.blogspot.com.au/2013/09/the-gear-effect-vej-tidal-torquing.html

   

Wednesday, April 15, 2015

Scientific Publications and Presentations

UPDATED 16/04/2015

The following is a list of my recent scientific publications and presentations. I am placing the list on my blog so that others can have easy access.

2014

Wilson, I.R.G. Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?,  Pattern Recogn. Phys., 2, 75-93

2013

Wilson, I.R.G.: The Venus–Earth–Jupiter spin–orbit coupling 
modelPattern Recogn. Phys., 1, 147-158

Wilson, I.R.G., Long-Term Lunar Atmospheric Tides in the 
Southern Hemisphere, The Open Atmospheric Science Journal,
2013, 7, 51-76

http://benthamopen.com/contents/pdf/TOASCJ/TOASCJ-7-51.pdf


Wilson, I.R.G., 2013, Are Global Mean Temperatures 
Significantly Affected by Long-Term Lunar Atmospheric 
Tides? Energy & Environment, Vol 24,
No. 3 & 4, pp. 497 - 508



Wilson, I.R.G., 2013, Personal Submission to the Senate 
Committee on Recent Trends in and Preparedness for 
Extreme Weather Events, Submission No. 106


2012

Wilson, I.R.G.Lunar Tides and the Long-Term Variation 
of the Peak Latitude Anomaly of the Summer Sub-Tropical 
High Pressure Ridge over Eastern Australia
The Open Atmospheric Science Journal, 2012, 6, 49-60

Wilson, I.R.G., Changes in the Earth's Rotation in relation 
to the Barycenter and climatic effect.  Recent Global Changes 
of the Natural Environment. Vol. 3, Factors of Recent 
Global Changes. – M.: Scientific World, 2012. – 78 p. [In Russian].

This paper is the Russian translation of my 2011 paper
Are Changes in the Earth’s Rotation Rate Externally 
Driven and Do They Affect Climate? 
The General Science Journal, Dec 2011, 3811.

2011

Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation 
Rate Externally Driven and Do They Affect Climate? 
The General Science Journal, Dec 2011, 3811.



Wilson, I.R.G., 2011, Do Periodic peaks in the Planetary Tidal 
Forces Acting Upon the Sun Influence the Sunspot Cycle? 
The General Science Journal, Dec 2011, 3812.


[Note: This paper was actually written by October-November 2007 and submitted to the New Astronomy (peer-reviewed) Journal in early 2008 where it was rejected for publication. It was resubmitted to the (peer-reviewed) PASP Journal in 2009 where it was again rejected. The paper was eventually published in the (non-peer reviewed) General Science Journal in 2010.]

2010

N. Sidorenkov, I.R.G. Wilson and A.I. Kchlystov, 2009, The 
decadal variations in the geophysical processes and the 
asymmetries in the solar motion about the barycentre. 
Geophysical Research Abstracts Vol. 12, EGU2010-9559, 
2010. EGU General Assembly 2010 © Author(s) 2010


2009


Wilson, Ian R.G., 2009, Can We Predict the Next Indian 
Mega-Famine?, Energy and Environment, Vol 20, 
Numbers 1-2, pp. 11-24.

El Ninos and Extreme Proxigean Spring Tides

A lecture by Ian Wilson at the Natural Climate Change
Symposium in Melbourne on June 17th 2009.
2008

Wilson, I.R.G., Carter, B.D., and Waite, I.A., 2008
Does a Spin-Orbit Coupling Between the Sun and the 
Jovian Planets Govern the Solar Cycle?,
Publications of the Astronomical Society of Australia
2008, 25, 85 – 93.

  
N.S. Sidorenkov, Ian WilsonThe decadal fluctuations 
in the Earth’s rotation and in the climate characteristics
In: Proceedings of the "Journees 2008 Systemes de reference 
spatio-temporels", M. Soffel and N. Capitaine (eds.), 
Lohrmann-Observatorium and Observatoire de Paris. 
2009, pp. 174-177 
  

Which Came First? - The Chicken or the Egg?

A Presentation to the 2008 Annual General Meeting of the
Lavoisier Society by Ian Wilson

http://www.lavoisier.com.au/articles/greenhouse-science/solar-cycles/IanwilsonForum2008.pdf

2006


Wilson, I. R. G., 2006, Possible Evidence of the 
De Vries, Gleissberg and Hale Cycles in the Sun’s 
Barycentric Motion, Australian Institute of Physics 17th
National Congress 2006, Brisbane, 3rd -8th December 
2006 (No longer available on the web)

Thursday, January 1, 2015

The El Niños during New Moon Epoch 5 - 1963 to 1994


A detailed investigation of the precise alignments between the lunar synodic [lunar phase] cycle and the 31/62 year Perigee-Syzygy cycle between 1865 and 2014 shows that it naturally breaks up six 31 year epochs each of which has a distinctly different tidal property. The second 31 year interval starts with the precise alignment on the 15th of April 1870 with the subsequent epoch boundaries occurring every 31 years after that:

Epoch 1 - Prior to 15th April  1870
Epoch 2 - 15th April 1870 to 18th April 1901
Epoch 3 - 8th April 1901 to 20th April 1932
Epoch 4 - 20th April 1932 to 23rd April 1963
Epoch 5 - 23rd April 1963 to 25th April 1994
Epoch 6 - 25th April 1994 to 27th April 2025



The hypothesis that the 31/62 year seasonal tidal cycle plays a significant role in sequencing the triggering of El Niñevents leads one to reasonable expect that tidal effects for the following three epochs:

New Moon Epoch:
Epoch 1 - Prior to 15th April  1870
Epoch 3 - 8th April 1901 to 20th April 1932
Epoch 5 - 23rd April 1963 to 25th April 1994

[N.B. During these epochs, the peak seasonal tides are dominated by new moons that are    predominately in the northern hemisphere.]

should be noticeably different to its effects for these three epochs:

Full Moon Epochs:
Epoch 2 - 15th April 1870 to 18th April 1901
Epoch 4 - 20th April 1932 to 23rd April 1963
Epoch 6 - 25th April 1994 to 27th April 2025

[N.B. During these epochs. the peak seasonal tides are dominated by full moons that are predominately in the southern hemisphere.]
If we specifically look at the 31 year New Moon Epoch 5, we find that: 

Figures 1, 2, and 3 (below) show the Moon's distance from the Earth (in kilometres) at the times where it crosses the Earth's equator, for the years 1964 through to 1995.

Figure 1


  Figure 2


Figure 3



Superimposed on each of these figures are the seven strong(#) El Niño events that occurred during this time period. Table 1 summaries the dates (i.e year and month) for start of each of these seven strong El Niño events.

Table 1



# For the definition of a strong El Niño event go to part c) of:

http://astroclimateconnection.blogspot.com.au/2014/11/evidence-that-strong-el-nino-events-are_12.html

[* N.B. The 1969 El Niño event just falls short of the selection criterion for a strong El Niño event because it only last for three months. It has been included in Table 1 for completeness.]

Figures 1,2 and 3 clearly show that all of the eight El Niño events in this tidal epoch occur at times where the distance of the Moon as sequential crossings of the Earth's equator have almost the same value of ~ 382,000 km. In the years when this happens, the lunar line-of-apse is closely aligned with either the December or June Solstice. 

It is possible that this correlation could be dismissed as a coincidence. However, it is extremely unlikely that:

a)  during the other New Moon tidal epoch i.e. Epoch 3 - from the 8th April 1901 to 20th April 1932, El Niño events should also occur when  the lunar line-of-apse is closely aligned with either the December or June Solstice.

b) during the Full Moon tidal epochs i.e. Epoch 2 - 15th April 1870 to 18th April 1901; Epoch 4 - 20th April 1932 to 23rd April 1963; Epoch 6 - 25th April 1994 to 27th April 2025, El Nino events should occur when  the lunar line-of-apse is closely aligned with either the March or September Equinox.

The switch between timing of El Niño events, once every 31 years, at the same time that there is a switch from a New Moon tidal epoch to Full Moon tidal epoch, tell us that it is very likely that El Niño events, are in fact, triggered by the lunar tides.

Friday, November 28, 2014

Are the Strongest Lunar Perigean Spring Tides Commensurate with the Transit Cycle of Venus?


New peer-reviewed paper available for (free) download at:

http://www.pattern-recognition-in-physics.com/pub/prp-2-75-2014.pdf

Abstract

This study identifies the strongest Perigean spring tides that reoccur at roughly the same time in the seasonal calendar and shows how their repetition pattern, with respect to the tropical year, is closely synchronized with the 243 year transit cycle of Venus. It finds that whenever the pentagonal pattern for the inferior conjunctions of Venus and the Earth drifts through one of the nodes of Venus’ orbit, the 31/62 year Perigean spring tidal cycle simultaneously drifts through almost exactly the same days of the Gregorian year, over a period from 1 to 3000 A.D. Indeed, the drift of the 31/62 year tidal cycle with respect to the Gregorian calendar  almost perfectly matches the expected long-term drift between the Gregorian calendar and the tropical year. If the mean drift of the 31/62 Perigean spring tidal cycle is corrected for the expected long-term drift between the Gregorian calendar and the tropical year, then the long-term residual drift between: a) the 243 year drift-cycle of the pentagonal pattern for the inferior conjunctions of Venus and the Earth with respect to the nodes of Venus’s orbit and b) the 243 year drift-cycle of the strongest seasonal peak tides on the Earth (i.e. the 31/62 Perigean spring tidal cycle) with respect to the tropical year is approximately equal to -7 ± 11 hours, over the 3000 year period. The large relative error of the final value for the residual drift means that this study cannot rule out the possibility that there is no long-term residual drift between the two cycles i.e. the two cycles are in perfect synchronization over the 3000 year period. However, the most likely result is a long-term residual drift of -7 hours, over the time frame considered.

Figure 13a


Figure 13b

Figure 13. The red curve in [a] shows the difference (in hours) between the tropical year and the Gregorian calendar year (measured from J2000), as calculated from equation (2) versus the year. This difference is subtracted from the measured mean drift displayed [a] to determine the long-term residual drift (in hours) versus the year, which is re-plotted in [b]. The ± 95 % confidence intervals for the measured mean drift [a] and the long-term residual drift [b] are displayed – see text for details.

Conclusion


This study identifies the strongest Perigean spring tides that reoccur at roughly the same time in the seasonal calendar and shows how their repetition pattern, with respect to the tropical year, is in near-resonance with the 243 year transit cycle of Venus.

A single representative time is determined for each of the transits (or transit pairs) of Venus, over the period from 1 to 3000 A.D., in order to delineate the 243 year transit cycle. The representative time chosen  for the transit cycle is the precise time of passage of  the drifting pattern for the inferior conjunctions of Venus and the Earth (i.e. the pentagram pattern seen in figure 1), through a given node of Venus’ orbit.


Two methods are used to determine the dates of these particular events, over the 3000 year period of the study:

1. The first involves finding the date on which the percent age fraction of the circular disk of Venus that is illuminated by the Sun (as seen by a geocentric observer) is a minimum.

2. The second method involves using the transits (or near transits) on either side of a given node of Venus’ orbit to determine the temporal drift rate (in solar latitude) for the pattern of inferior conjunctions of Venus and the Earth. This is then used to calculate the date on which the pattern crosses the solar equator.

A selection process is set up to identify all new/full moons that occur within ± 20 hours of perigee, between the (Gregorian) calendar dates of the 14th of December and the 11th of January, spanning the years from 1 A.D. to 3000 A.D. This process successfully identifies all of the spring tidal events with equilibrium ocean tidal heights greater than approximately 62.0 cm, over the time interval chosen. These events are designated as the sample tidal events or the sample tides. Four distinct peak tidal cycles with periodicities less than 100 years are identified amongst the sample tides.

Investigations of these peak tidal cycles reveal that the 31/62 year tidal cycle is best synchronized to the seasonal calendar, over centennial time scales. Sequential events in this tidal cycle move forward through the seasonal calendar by only 2 – 3 days every 31 years, and the number of hours between new/full moon and perigee (a measure of their peak tidal strength) only changes by ~ 0.6 hours every 31 years.

An analysis of the 31/62 lunar peak tidal cycle shows that the sample tidal events reoccur on almost the same day of Gregorian (seasonal) calendar after 106 years, and then they reoccur on almost the same day after another 137 years. This produces a two-stage long-term repetition cycle with a total length of (106 + 137 years =) 243 years.

Remarkably, this means that, whenever the pentagonal pattern for the inferior conjunctions of Venus and the Earth drifts through one of the nodes of Venus’ orbit, the 31/62 year Perigean spring tidal cycle simultaneously drifts through almost exactly the same days of the Gregorian year, over a period of almost three thousand years. Indeed, the drift of the 31/62 year tidal cycle with respect to the Gregorian calendar almost perfectly matches the expected long-term drift between the Gregorian calendar and the tropical year. If the mean drift of the 31/62 Perigean spring tidal cycle is corrected for the expected long-term drift between the Gregorian calendar and the tropical year, then the long-term residual drift between:

1. the 243 year drift-cycle of the pentagonal pattern for the inferior conjunctions of Venus
and the Earth with respect to the nodes of Venus’s orbit

and

2. the 243 year drift-cycle of the strongest seasonal peak tides on the Earth (i.e. the 31/62 Perigean spring tidal cycle) with respect to the tropical year

is approximately equal to -7 ± 11 hours, over a 3000 years period. The large relative error of the final value for the residual drift means that this study cannot rule out the possibility that there is no long-term residual drift between the two cycles i.e. the two cycles are in perfect synchronization over the 3000year period from 1 to 3000 A.D. However, the most likely result is a long-term residual drift of -7 hours, over the time frame considered. Finally, there is one speculative extrapolation that could encourage others to further investigate this close synchronization on much longer time scales. If these future investigations show that the long-term residual drift rate of -7 hours over 3000 years is valid over much longer time scales then this close synchronization may highlight a mechanism that might be responsible for the Earth’s 100,000 year Ice-Age cycle. This comes from the fact that the strongest Perigean spring tides would be in close synchronization with (i.e. ± half a day either side of) the date of the Earth’s Solstice (on or about December 21st) for a period (24/7) × 3000 years =10,300 years. In addition, this close synchronization would be re-established itself after the 31/62 peak tidal pattern drifted backward through the Tropical calendar by ~ 9.7 days (i.e. the average vertical spacing between sequences in figs 12a & b) such that after ((9.7 × 24) / 7) × 3000 years = 99,800 years.

Hence, the close synchronization discovered in this study lasts for ~10,000 years, with each period of close synchronization being separated from its predecessor by ~100,000 years. This is very reminiscent of the inter-glacial/glacial period that is characteristic of the Earth’s recent Ice-Age cycles.